In this post I would like to make an argument which I believe to be significant. It all starts from a question: how many images can be represented? Or: is there a number that expresses the maximum amount of images that can exist?

At first, it seems one of those dilemmas that is clearly impossible to answer, e.g. “how many grains of sand are there on Earth?” or “how many water drops are there in the sea?” Yes, there is a finite number of grains of sand or drops of water on our planet, but it is practically impossible to have the exact number, count them with accuracy. An estimate can be made, an approximation.

But, instead, speaking of images, we know that number. It’s a calculable amount, and that’s what I’m going to do now.

Let’s start from the assumption that each image is a set of points, called pixels, so the more pixels an image has, the higher its resolution. If for example it has 1000 pixels horizontally and 1000 pixels vertically, the total number will be 1000×1000 = 1 million pixels, abbreviated to 1 mega-pixel. Today, modern smartphones are equipped with cameras of more than 10 megapixels, with around 3,000 pixels on each side.

 

In the picture above, of just 24×24 pixels, a fish is represented: its shape is barely distinguishable. If one wanted to represent the traits of a person, much more space would be needed.

To calculate the number of all the images that can exist, it is first of all necessary to establish what resolution these images must be. Suppose 64×64 (4096 pixels), the minimum to distinguish a face within a photo.

Then we need to establish which color depth to use. “Normal” photos, those made by smartphones, are in color and each pixel is indicated by three values ​​between 0 and 255 corresponding respectively to a shade of red, green and blue. Each pixel is therefore represented by three digits (eg: 3.10.45). This color standard is called truecolor or 24bit.

A black and white image, on the other hand, takes up much less information. Each pixel is indicated by a single digit, so that the overall weight of the file decreases by one third. The black and white depth is also called 8bit, or greyscale , and uses shades of gray to describe the colors.

If desired, one can save even more space by using the 1-bit color standard, called monochrome , (one color). This format records every pixel as 0 or 1: if it is 0 it will correspond to white, if it is 1 to black. This creates a much less clear image than a black and white one, but still capable of representing an object.
I already know that the number I’m going to calculate will be very large, so I have to be a bit stingy and choose the 1bit format so that we can write it on this page without overdoing it.

 

 

 

 

 

What then is the exact number of images that can exist at 1bit and with a 64×64 pixel resolution?

It is about raising the possible colors of 1bit (2) to a power that is the number of pixels of the image (4096). The result is the following:

 

1 044 388 881 413 152 506 691 752 710 716 624 382 579 964 249 047 383 780 384 233 483 283 953 907 971 557 456 848 826 811 934 997 558 340 890 106 714 439 262 837 987 573 438 185 793 607 263 236 087 851 365 277 945 956 976 543 709 998 340 361 590 134 383 718 314 428 070 011 855 946 226 376 318 839 397 712 745 672 334 684 344 586 617 496 807 908 705 803 704 071 284 048 740 118 609 114 467 977 783 598 029 006 686 938 976 881 787 785 946 905 630 190 260 940 599 579 453 432 823 469 303 026 696 443 059 025 015 972 399 867 714 215 541 693 835 559 885 291 486 318 237 914 434 496 734 087 811 872 639 496 475 100 189 041 349 008 417 061 675 093 668 333 850 551 032 972 088 269 550 769 983 616 369 411 933 015 213 796 825 837 188 091 833 656 751 221 318 492 846 368 125 550 225 998 300 412 344 784 862 595 674 492 194 617 023 806 505 913 245 610 825 731 835 380 087 608 622 102 834 270 197 698 202 313 169 017 678 006 675 195 485 079 921 636 419 370 285 375 124 784 014 907 159 135 459 982 790 513 399 611 551 794 271 106 831 134 090 584 272 884 279 791 554 849 782 954 323 534 517 065 223 269 061 394 905 987 693 002 122 963 395 687 782 878 948 440 616 007 412 945 674 919 823 050 571 642 377 154 816 321 380 631 045 902 916 136 926 708 342 856 440 730 447 899 971 901 781 465 763 473 223 850 267 253 059 899 795 996 090 799 469 201 774 624 817 718 449 867 455 659 250 178 329 070 473 119 433 165 550 807 568 221 846 571 746 373 296 884 912 819 520 317 457 002 440 926 616 910 874 148 385 078 411 929 804 522 981 857 338 977 648 103 126 085 903 001 302 413 467 189 726 673 216 491 511 131 602 920 781 738 033 436 090 243 804 708 340 403 154 190 336